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Here, we present an overview of a first principles homogenization theory ofperiodic metamaterials. It is shown that in a rather general context it ispossible to formally introduce effective parameters that describe the timeevolution of macroscopic (slowly-varying in space) initial states of theelectromagnetic field using an effective medium formalism. The theory isapplied to different types of "wire metamaterials" characterized by a strongspatial dispersion in the long wavelength limit. It is highlighted that thespatial dispersion may tailor in unique ways the wave phenomena in wiremetamaterials leading to exotic tunneling effects and broadband losslessanomalous dispersion.

First Principles Homogenization of Periodic Metamaterials and Application to Wire Media